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Putnam
1958 November Putnam
A6
A6
Part of
1958 November Putnam
Problems
(1)
Putnam 1958 November A6
Source: Putnam 1958 November
7/19/2022
Let
a
(
x
)
a(x)
a
(
x
)
and
b
(
x
)
b(x)
b
(
x
)
be continuous functions on
[
0
,
1
]
[0,1]
[
0
,
1
]
and let
0
≤
a
(
x
)
≤
a
<
1
0 \leq a(x) \leq a <1
0
≤
a
(
x
)
≤
a
<
1
on that range. Under what other conditions (if any) is the solution of the equation for
u
,
u,
u
,
u
=
max
0
≤
x
≤
1
b
(
x
)
+
a
(
x
)
u
u= \max_{0 \leq x \leq 1} b(x) +a(x)u
u
=
0
≤
x
≤
1
max
b
(
x
)
+
a
(
x
)
u
given by
u
=
max
0
≤
x
≤
1
b
(
x
)
1
−
a
(
x
)
.
u = \max_{0 \leq x \leq 1} \frac{b(x)}{1-a(x)}.
u
=
0
≤
x
≤
1
max
1
−
a
(
x
)
b
(
x
)
.
Putnam
function
maximum